Correlation analysis as a tool for economic and statistical research

Correlation analysis is a set of mathematically grounded methods by which the correlation dependence is found between a pair of factors or features having a random component. In the set of techniques used in this method of research, widespread:

- construction of correlation fields, compilation of correlation tables;

- calculation of the correlation ratio or sampling coefficients;

- testing the hypothesis of the statistical significance of links.

The continuation of the research leads to the establishment of specific types of interrelation between the quantities. The relationship between random characters or factors of more than three needs to use the multivariate analysis method.

The field and table, which are constructed by correlation analysis, are used as auxiliary tools in the analysis of sample data. By applying selective points on the coordinate plane field, we come to the so-called correlation field. By how the points are located, you can already make a preliminary forecast and determine the form of the dependence of random variables. Numerical processing of the results requires grouping them in the form of a correlation table.

First appearing in the 18th century, the term "correlation" with the light hand of paleontologist Georges Cuvier began to be actively used for the process of restoring the appearance of fossil animals to parts of its remains. The development of a narrowly directed paleontological method led to the fact that the correlation analysis began to be used in the most diverse spheres of human life activity.

This method is attractive for the processing of statistical data. The correlation analysis in statistics was first used by the English biologist and statistician Francis Galton at the end of the 19th century. In the future, the development of the method made it possible to measure the tightness of the connection between a pair and a large number of variables. Correlation analysis has a close relationship with regression analysis.

Correlation analysis in the economy takes a special place. But its use imposes a number of limitations. First of all, this is the presence of a sufficient number of measurements and data for study. Practice suggests that the number of observations should exceed by 5-6 times the number of factors. The optimal option is the presence of a number of observations exceeding the number of factors several dozen times. In this case, the law of large numbers operates, thanks to it there will be an inter-extinction of random oscillations.

Also, it is necessary to ensure that the entire set of factor and performance traits is subject to a normal multidimensional distribution. There are cases when the volume of the aggregate is not enough to perform a formal test for compliance with the normality of the distribution, then the definition of the distribution law is visually performed according to the correlation field data. If the points are arranged according to a linear trend, then it is quite realistic to conclude that the set of initial data will satisfy the requirements of the normal distribution law.

In the initial set of values, it is necessary to monitor the qualitative homogeneity.

The presence of the fact of the correlation dependence does not give grounds for the assertion that an arbitrarily taken variable precedes the appearance of the second or causes its changes, in other words, there is no strict causal relationship between them, and even the operation of some third factor is possible.

Applying the results of analysis in practice on the basis of correlation methods of research, it is possible to draw a number of definite conclusions about the presence, and most importantly, the nature of interdependence. This already gives a weighty share of information about the object under investigation.